Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

When positive integer n is divided by 3, the remainder is 2 [#permalink]
01 Nov 2009, 12:06

1

This post received KUDOS

5

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

61% (02:00) correct
39% (02:08) wrong based on 179 sessions

When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

(1) n-2 is divisible by 5. (2) t is divisible by 3.

"If you want my advice, Peter," he said at last, "you've made a mistake already. By asking me. By asking anyone. Never ask people. Not about your work. Don't you know what you want? How can you stand it, not to know?" Ayn Rand

Re: GMAT Prep 2 remainder [#permalink]
01 Nov 2009, 13:07

1

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

(1) n-2 is divisible by 5. (2) t is divisible by 3.

From the stem: n=3p+2 and t=5q+3. nt=15pq+9p+10q+6, we should find the remainder when this expression is divided by 15.

(1) n-2=5m --> n=5m+2=3p+2 --> 5m=3p, 15m=9p --> nt=15pq+9p+10q+6=15pq+15m+10q+6. Clearly 15pq and 15m are divisible by 15, so remainder by dividing these components will be 0. But we still know nothing about 10q+6. Not sufficient.

(2) t is divisible by 3 means that 5q+3 is divisible by 3 --> 5q is divisible by 3 or q is divisible by 3 --> 5q=5*3z=15z --> 10q=30z --> nt=15pq+9p+10q+6=15pq+9p+30z+6. 15pq and 30z are divisible by 15. Know nothing about 9p+6. Not sufficient.

(1)+(2) 9p=15m and 10q=30z --> nt=15pq+9p+10q+6=15pq+15m+30z+6. Remainder when this expression is divided by 15 is 6. Sufficient.

Answer: C.

OR:

From the stem: n=3p+2 and t=5q+3.

(1) n-2 is divisible by 5 --> n-2=5m --> n=5m+2 and n=3p+2 --> general formula for n would be n=15k+2 (about deriving general formula for such problems at: good-problem-90442.html#p723049 and manhattan-remainder-problem-93752.html#p721341) --> nt=(15k+2)(5q+3)=15*5kq+15*3k+10q+6 --> first two terms are divisible by 15 (15*5kq+15*3k) but we don't know about the last two terms (10q+6). Not sufficient.

(2) t is divisible by 3 --> t=3r and t=5q+3 --> general formula for t would be t=15x+3 --> nt=(3p+2)(15x+3)=15*3px+9p+15*2x+6. Not sufficient.

(1)+(2) nt=(15k+2)(15x+3)=15*15kx+15*3k+15*2x+6 this expression divided by 15 yields remainder of 6. Sufficient.

Re: GMAT Prep 2 remainder [#permalink]
24 May 2010, 16:52

If the explanation above is not helpful, you may find a step by step video solution of this question useful. On GMATFix site, this is GMATPrep question 1045

Re: DS problem : remainders [#permalink]
28 Nov 2010, 17:36

9

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

hogwarts wrote:

Saw this question on a GMATPrep test, and I can't figure out how to get to the correct answer. Can anyone help? Thanks!

When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

(1) n-2 is divisible by 5. (2) t is divisible by 3.

The correct answer is (C) - both statements together are sufficient, but neither statement alone is sufficient. Can anybody out there help explain to me how to get to this answer though? Thanks!

This is how I would approach this question.

When positive integer n is divided by 3, the remainder is 2; I say n = 3a + 2 ( a is a non negative integer)

and when positive integer t is divided by 5, the remainder is 3. So t = 5b + 3 (b is a non negative integer.)

What is the remainder when the product nt is divided by 15? So nt = (3a + 2)(5b + 3) = 15ab + 9a + 10b + 6 15ab is divisible by 15. But I don't know anything about (9a + 10b + 6) yet.

Stmnt 1: n-2 is divisible by 5. From above, n - 2 is just 3a. If n - 2 is divisible by 5, then 'a' must be divisible by 5. So I get that 9a is divisible by 15. I still don't know anything about b. If b = 1, remainder of nt is 1. If b = 2, remainder of nt is 11 and so on... Not sufficient.

Stmnt 2: t is divisible by 3. If t is divisible by 3, then (5b + 3) is divisible by 3. Therefore, b must be divisible by 3. (If this is unclear, think: 15 + 3 will be divisible by 3 but 20 + 3 will not be. If the second term is 3, the first term must also be divisible by 3 to make the whole expression divisible by 3). So 10b is divisible by 15 but we do not know anything about a. If a = 1, remainder of nt is 0, if a = 2, remainder of nt is 9. Not sufficient.

Using both statements together, we know 9a and 10b are divisible by 15. So remainder must be 6. Sufficient.

Re: GMAT Prep 2 remainder [#permalink]
15 Mar 2011, 23:55

1

This post received KUDOS

Bunuel wrote:

When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

(1) n-2 is divisible by 5. (2) t is divisible by 3.

Answer: C.

I have another approach to this ds, plz correct me if i'm wrong. n=3x + 2 t = 5y + 3 Clearly we cannot solve the problem with either n or t. We need both information concerning n and t because we need to figure out the remaining of n*t. => left with C or E

(1): n-2 is divisible by 5 & n=3x + 2 => x is multiple of 5. (2): t is divisible by 3. & t = 5y + 3 => y is multiple of 3 (1)& (2) => n*t = (3x+2) (5y+3) = (3x*5y) + (9x) + (10y) + 6 we know that: x is multiple of 5, y is multiple of 3 so: (3x*5y) + (9x) + (10y) + 6 will have remaining of 6 because: each (3x*5y); (9x); (10y) is all multiple of 15. _________________

Consider giving me kudos if you find my explanations helpful so i can learn how to express ideas to people more understandable.

Re: When positive integer n is divided by 3, the remainder is 2 [#permalink]
07 Oct 2013, 20:15

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: DS problem : remainders [#permalink]
19 Oct 2013, 07:00

VeritasPrepKarishma wrote:

hogwarts wrote:

Saw this question on a GMATPrep test, and I can't figure out how to get to the correct answer. Can anyone help? Thanks!

When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

(1) n-2 is divisible by 5. (2) t is divisible by 3.

The correct answer is (C) - both statements together are sufficient, but neither statement alone is sufficient. Can anybody out there help explain to me how to get to this answer though? Thanks!

This is how I would approach this question.

When positive integer n is divided by 3, the remainder is 2; I say n = 3a + 2 ( a is a non negative integer)

and when positive integer t is divided by 5, the remainder is 3. So t = 5b + 3 (b is a non negative integer.)

What is the remainder when the product nt is divided by 15? So nt = (3a + 2)(5b + 3) = 15ab + 9a + 10b + 6 15ab is divisible by 15. But I don't know anything about (9a + 10b + 6) yet.

Stmnt 1: n-2 is divisible by 5. From above, n - 2 is just 3a. If n - 2 is divisible by 5, then 'a' must be divisible by 5. So I get that 9a is divisible by 15. I still don't know anything about b. If b = 1, remainder of nt is 1. If b = 2, remainder of nt is 11 and so on... Not sufficient.

Stmnt 2: t is divisible by 3. If t is divisible by 3, then (5b + 3) is divisible by 3. Therefore, b must be divisible by 3. (If this is unclear, think: 15 + 3 will be divisible by 3 but 20 + 3 will not be. If the second term is 3, the first term must also be divisible by 3 to make the whole expression divisible by 3). So 10b is divisible by 15 but we do not know anything about a. If a = 1, remainder of nt is 0, if a = 2, remainder of nt is 9. Not sufficient.

Using both statements together, we know 9a and 10b are divisible by 15. So remainder must be 6. Sufficient.

Answer (C).

so from statement 1 we got 10b+6 if b=1 we get 16 then rem =1 if b=2 we got 106 so remainder =1 if b=3 we get 1006 so remainder =1 ..............................so i think a is sufficient .............what am i doing wrong

Re: DS problem : remainders [#permalink]
20 Oct 2013, 04:38

1

This post received KUDOS

Expert's post

tyagigar wrote:

VeritasPrepKarishma wrote:

hogwarts wrote:

Saw this question on a GMATPrep test, and I can't figure out how to get to the correct answer. Can anyone help? Thanks!

When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

(1) n-2 is divisible by 5. (2) t is divisible by 3.

The correct answer is (C) - both statements together are sufficient, but neither statement alone is sufficient. Can anybody out there help explain to me how to get to this answer though? Thanks!

This is how I would approach this question.

When positive integer n is divided by 3, the remainder is 2; I say n = 3a + 2 ( a is a non negative integer)

and when positive integer t is divided by 5, the remainder is 3. So t = 5b + 3 (b is a non negative integer.)

What is the remainder when the product nt is divided by 15? So nt = (3a + 2)(5b + 3) = 15ab + 9a + 10b + 6 15ab is divisible by 15. But I don't know anything about (9a + 10b + 6) yet.

Stmnt 1: n-2 is divisible by 5. From above, n - 2 is just 3a. If n - 2 is divisible by 5, then 'a' must be divisible by 5. So I get that 9a is divisible by 15. I still don't know anything about b. If b = 1, remainder of nt is 1. If b = 2, remainder of nt is 11 and so on... Not sufficient.

Stmnt 2: t is divisible by 3. If t is divisible by 3, then (5b + 3) is divisible by 3. Therefore, b must be divisible by 3. (If this is unclear, think: 15 + 3 will be divisible by 3 but 20 + 3 will not be. If the second term is 3, the first term must also be divisible by 3 to make the whole expression divisible by 3). So 10b is divisible by 15 but we do not know anything about a. If a = 1, remainder of nt is 0, if a = 2, remainder of nt is 9. Not sufficient.

Using both statements together, we know 9a and 10b are divisible by 15. So remainder must be 6. Sufficient.

Answer (C).

so from statement 1 we got 10b+6 if b=1 we get 16 then rem =1 if b=2 we got 106 so remainder =1 if b=3 we get 1006 so remainder =1 ..............................so i think a is sufficient .............what am i doing wrong

10b above means 10*b, 10 multiplied by b.

If b=2, then 10b+6=10*2+6=26 not 106; If b=2, then 10b+6=10*3+6=36 not 1006.

Re: When positive integer n is divided by 3, the remainder is 2 [#permalink]
27 Oct 2014, 22:58

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

I´ve done an interview at Accepted.com quite a while ago and if any of you are interested, here is the link . I´m through my preparation of my second...

It’s here. Internship season. The key is on searching and applying for the jobs that you feel confident working on, not doing something out of pressure. Rotman has...